# How do you solve 3^(x^2) + 4x = 1/27?

##### 1 Answer
May 7, 2018

$x \approx - 1.2 , - 0.26$

#### Explanation:

This is called a transcendental equation and therefore does not generally have a simple/exact solution. This is because of the x in the exponential and the coefficient. For example, ${e}^{x} = x$ doesn't have an analytical solution, just a numerical one.

Generally, the best method of solving these is Newton's method, numerically approximating the solution.

In this case, it is pretty easy for a calculator to find that there is a solution around -1.2 and one around -0.26.